[tex]\bf \qquad \qquad \textit{inverse proportional variation}
\\\\
\textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------[/tex]
[tex]\bf \stackrel{\textit{time \underline{t} required to drive a certain distance varies inversely with the speed \underline{r}}}{t=\cfrac{k}{r}}
\\\\\\
\textit{we also know that }
\begin{cases}
t=4\\
r=35
\end{cases}\implies 4=\cfrac{k}{35}\implies 4(35)=k
\\\\\\
140=k\qquad therefore\qquad \boxed{t=\cfrac{140}{r}}
\\\\\\
\textit{now, when \underline{r} = 45, what is \underline{t}?}\qquad t=\cfrac{140}{45}[/tex]
